Drop Oscillations Research Articles

Dynamics of sessile and pendant drops excited by surface acoustic waves: Gravity effects and correlation between oscillatory and translational motions.

When sessile droplets are excited by ultrasonic traveling surface acoustic waves (SAWs), they undergo complex dynamics with both oscillations and translational motion. While the nature of the Rayleigh-Lamb quadrupolar drop oscillations has been identified, their origin and their influence on the drop mobility remains unexplained. Indeed, the physics behind this peculiar dynamics is complex with nonlinearities involved both at the excitation level (acoustic streaming and radiation pressure) and in the droplet response (nonlinear oscillations and contact line dynamics). In this paper, we investigate the dynamics of sessile and pendant drops excited by SAWs. For pendant drops, so-far unreported dynamics are observed close to the drop detachment threshold with the suppression of the translational motion. Away from this threshold, the comparison between pendant and sessile drop dynamics allows us to identify the role played by gravity or, more generally, by an initial or dynamically induced stretching of the drop. In turn, we elucidate the origin of the resonance frequency shift, as well as the origin of the strong correlation between oscillatory and translational motion. We show that for sessile drops, the velocity is mainly determined by the amplitude of oscillation and that the saturation observed is due to the nonlinear dependence of the drop response frequency on the dynamically induced stretching.

A ghost fluid method for sharp interface simulations of compressible multiphase flows

A ghost fluid based computational tool is developed to study a wide range of compressible multiphase flows involving strong shocks and contact discontinuities while accounting for surface tension, viscous stresses and gravitational forces. The solver utilizes constrained reinitialization method to predict the interface configuration at each time step. Surface tension effect is handled via an exact interface Riemann problem solver. Interfacial viscous stresses are approximated by considering continuous velocity and viscous stress across the interface. To assess the performance of the solver several benchmark problems are considered: One-dimensional gas-water shock tube problem, shock-bubble interaction, air cavity collapse in water, underwater explosion, Rayleigh-Taylor Instability, and ellipsoidal drop oscillations. Results obtained from the numerical simulations indicate that the numerical methodology performs reasonably well in predicting flow features and exhibit a very good agreement with prior experimental and numerical observations. To further examine the accuracy of the developed ghost fluid solver, the obtained results are compared to those by a conventional diffuse interface solver. The comparison shows the capability of our ghost fluid method in reproducing the experimentally observed flow characteristics while revealing more details regarding topological changes of the interface.

Dynamic characteristics of the recessed chamber within a gas–liquid coaxial injector

In this article, a linear dynamic characteristic model of the recessed chamber in a gas–liquid shear coaxial injector is developed. The gaseous injector flow before the recessed chamber is considered to be steady, and we just investigate the response of pressure drop across the recessed chamber to the mass flow rate fluctuation of the liquid injector. The transfer function of the recessed chamber is obtained, considering the distribute characteristics of liquid droplets within the recessed chamber. The results show that the amplitude of pressure drop pulsation would decrease as the liquid flow pulsation frequency increases, when the variation of liquid velocity is not taken into account. While considering the variation of liquid velocity, the result is opposite. The amplitude of pressure drop oscillation on the boundary of the recessed chamber increases with the increase in liquid velocity oscillation frequency.

Two-phase flow instabilities of forced circulation at low pressure in a rectangular mini-channel

An experimental study has been carried out in a rectangular mini-channel to investigate the two-phase flow instabilities of a forced flow at low pressure. The inlet mass flux is gradually reduced by decreasing the rotational speed of the primary pump until the flow becomes unstable, while maintaining all other thermal parameters including system pressure, inlet temperature and heat flux unchanged. Three types of flow instabilities, density wave oscillation (DWO), pressure drop oscillation (PDO) and Ledinegg instability (LED) are identified during the experiment. The onset of flow instability (OFI) is determined by the demand curves and shows good agreement with Roach and Stoddard’s correlations. The OFI is consistent with the boiling incipience and saturated condition. The stability map is obtained on the plane of subcooling number (Nsub) and phase change number (Npch). DWO and PDO occur at the region between the outlet steam quality xe=−0.001 and xe=0.012, while the LED region becomes narrow with increasing subcooling. Finally, the mechanisms of flow instabilities in our experiment are analyzed. The results show that the PDO observed in this work is not accompanied by CHF (dryout) which is supposed to be the most common phenomenon of flow instabilities in mini-/micro-channels. DWO occurrence is determined by the relation between external forces (gravitational force and pump driving force) and surface tension. As the external forces are dominant, Type-I DWO at low outlet steam quality (DWOI) occurs. However, with reduction of the inlet mass flux, the surface tension begins to play a dominant role. Thus Type-II DWO at high outlet quality (DWOII), which is expected in most ordinarily sized channels, has not been observed during this work.

Some Aspects of Interfacial Phenomena in Steelmaking and Refining

Unique experiments were designed to study the surface phenomena in steelmaking reactions. The concept of surface sulfide capacities and an understanding of the surface accumulation of surface-active species, based on experimental results, are presented. In order to understand the flow phenomenon at slag/metal interface, experiments were designed to measure the interfacial velocity of S on the surface of an iron drop immersed in an aluminosilicate slag using the X-ray sessile drop method. The oscillation of the iron drop in the slag due to the change in the surface concentration of sulfur at the slag–metal interface was monitored by X-ray imaging. From the observations, the interfacial velocity of sulfur was evaluated. Similar experiments were performed to measure the interfacial velocity of oxygen at the interface as well as the impact of oxygen potential on the interfacial velocity of sulfur. The interfacial shear viscosity and the dilatational modulus were also evaluated. In a study of the wetting of alumina base by iron drop at constant oxygen pressure under isothermal condition, the contact angle was found to be decreased with the progress of the reaction leading to the formation of hercynite as an intermediate layer creating non-wetting conditions. In the case of silica substrate, an intermediate liquid fayalite layer was formed.

On the use of AC electrowetting for biosensing based on dynamic contact angle

A model system based on bovine serum albumin (BSA)-laden drop is selected. AC ElectroWetting-On-Dielectrics (EWOD), increasingly used in digital microfluidics for medical assays, is implemented in coplanar configuration. The moderate frequency required by EWOD actuation enables shape oscillations of the BSA-laden sessile drop and promotes internal micro-streaming. The non-reversible impact of EWOD-induced micro-streaming upon surface pressures is investigated. In contrast to the liquid–gas drop surface where thermodynamical equilibrium is instantaneously achieved, the adsorption of BSA molecules at the lubricated solid substrate can be characterized by a time-dependent solid–liquid surface pressure. As demonstrated from dynamic contact angle (DCA) imaging, adsorption of BSA is promoted under AC EWOD. A significant dependence of the solid–liquid surface pressure on the resonant capillary frequencies is observed: for a large enough actuation frequency corresponding to an oscillating mode, n=6, numerical simulations are performed which show that corner eddies located in the Stuart boundary layer, near the oscillating contact line, yield an efficient molecular renewal. In this way, oscillating EWOD could be used purposely as a tool to speed up label-free detection from DCA measurements.

Electromagnetic radiation due to nonlinear oscillations of a charged drop

The nonlinear oscillations of a spherical charged drop are asymptotically analyzed under the conditions of a multimode initial deformation of its equilibrium shape. It is found that if the spectrum of initially excited modes contains two adjacent modes, the translation mode of oscillations is excited among others. In this case, the center of the drop’s charge oscillates about the equilibrium position, generating a dipole electromagnetic radiation. It is shown that the intensity of this radiation is many orders of magnitude higher than the intensity of the drop’s radiation, which arises in calculations of the first order of smallness and is related to the drop’s charged surface oscillations.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding.

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

The oscillations of cylindrical drop under the influence of a nonuniform alternating electric field

The forced oscillations of incompressible fluid drop under the alternating electric field are considered. In equilibrium, the drop has the form of a cylinder bounded axially parallel solid planes and contact angle is right. The drop is surrounded by an incompressible fluid with another density. The external nonuniform electric field acts as an external force that causes motion of the contact line. In order to describe this contact line motion the modified Hocking boundary condition is applied: the velocity of the contact line is proportional to the deviation of the contact angle and the speed of the fast relaxation processes, which frequency is proportional

Axisymmetric oscillations of a cylindrical drop in the final volume of fluid

The eigen and forced oscillations of a fluid drop surrounded by an incompressible fluid in a cylindrical container of a final volume are considered. The drop has a cylindrical shape in equilibrium and is bounded axially by two parallel solid surfaces. The equilibrium contact angle is a right angle. Dynamics of the contact line is taken into account by setting an effective boundary condition derived by Hocking: velocity of the contact line is assumed to be proportional to deviation of the contact angle from the equilibrium value. This condition leads to oscillation damping, which arises from the interaction of the contact line with a solid surface. Hocking’s parameter (wetting parameter) is the proportionality coefficient in this condition. A completely pinned contact line (pinned-end edge condition) corresponds to the limiting value of Hocking’s parameter, which tends to zero. Hocking’s parameter tends to infinity in the opposite case of the fixed contact angle. The solution of the boundary value problem is found using Fourier series of Laplace operator eigenfunctions. Dependence of the eigenfrequency and damping rates on the problem parameters is investigated. It has been established that the main frequency of free oscillations can vanish at a certain value of Hocking’s parameter (so-called wetting parameter). The length of this interval depends on the ratio of height to radius of the drop. Other frequencies decrease monotonically with increasing Hocking’s parameter. The values of all frequencies increase with increasing relative radius of the drop or the radius of the vessel. Well-marked resonance effects are found in the study of forced oscillations. For the case of a pinned contact line or a fixed contact angle, the amplitude of forced oscillations grows without bound near the eigenfrequency. In other cases, the amplitude is finite. There are “anti-resonant” frequencies at which no deviation of the contact line from the equilibrium value is observed at any values of Hocking's parameter.

Translational oscillations of a cylindrical drop in a bounded volume of fluid

We consider the eigen and forced translational oscillations of a fluid drop surrounded by another fluid in a cylindrical vessel of finite volume. The drop is cylindrical in equilibrium and bounded axially by two parallel solid planes. Our approach takes into account the contact line dynamics of three continuous media (drop-liquid-solid surface), namely the velocity of the contact line proportional to the deviation of the contact angle from its equilibrium value. The Hocking’s parameter (so-called wetting parameter) is the proportionality coefficient in this case. A completely pinned contact line (so-called pinned-end edge condition) corresponds to the limiting value of Hocking’s parameter, which tends to zero. Hocking’s parameter tends to infinity in the opposite case of the fixed contact angle. The solution of the boundary value problem is found using Fourier series of Laplace operator eigen functions. The vibration force is directed along the symmetry axis of the drop. It is shown that the fundamental frequency of the translational mode of free oscillations vanishes at a critical value of Hocking’s parameter. Increasing the density of the drop or the radius of the vessel leads to the growth of the frequencies of eigenoscillations. The frequencies of the heavy drop (i.e. the drop having the density greater than that of the surrounding fluid) also increase with increasing relative radius of the drop, and for the light drop they decrease. We have revealed the existence of resonance effects for forced oscillations. The oscillation amplitude of the contact line is always finite, but the oscillation amplitude of the drop lateral surface tends to infinity in the zero limit of Hocking’s parameter. There are “anti-resonant” frequencies at which no deviation of the contact line from the equilibrium value is observed for any values of Hocking's parameter.

Linear (in oscillation dimensionless amplitude) interaction between the modes of a nonspherical charged drop in an external electrostatic field

The stability of a heavily charged drop in a weak uniform electrostatic field (in which the equilibrium shape of the drop can be represented by a prolate spheroid) is calculated in the fourth order of smallness in the eccentricity of the spheroidal drop and in the first order of smallness in the drop oscillation dimensionless amplitude. It is found that as the order of approximation in eccentricity grows, so does the number of modes interacting with the initially excited mode. In the given order of smallness, the preferred (initially excited) mode is shown to interact with the nearest eight modes. The drop becomes unstable if such is the second mode.

Optimal location of advance warning for mandatory lane change near a two-lane highway off-ramp

Improper mandatory lane change (MLC) maneuvers in the vicinity of highway off-ramp will jeopardize traffic efficiency and safety. Providing an advance warning for lane change necessity is one of the efficient methods to perform systematic lane change management, which encourages smooth MLC maneuvers occurring at proper locations to mitigate the negative effects of MLC maneuvers on traffic flow nearby off-ramp. However, the state of the art indicates the lack of rigorous methods to optimally locate this advance warning so that the maximum benefit can be obtained. This research is motivated to address this gap. Specifically, the proposed approach considers that the area downstream of the advance warning includes two zones: (i) the green zone whose traffic ensures safe and smooth lane changes without speed deceleration (S-MLC); the start point of the green zone corresponding to the location of the advance warning; (ii) the yellow zone whose traffic leads to rush lane change maneuvers with speed deceleration (D-MLC). An optimization model is proposed to search for the optimal green and yellow zones. Traffic flow theory such as Greenshield model and shock wave analysis are used to analyze the impacts of the S-MLC and D-MLC maneuvers on the traffic delay. A grid search algorithm is applied to solve the optimization model. Numerical experiments conducted on the simulation model developed in Paramics 6.9.3 indicate that the proposed optimization model can identify the optimal location to set the advance MLC warning nearby an off-ramp so that the traffic delay resulting from lane change maneuvers is minimized, and the corresponding capacity drop and traffic oscillation can be efficiently mitigated. Moreover, the experiments validated the consistency of the green and yellow zones obtained in the simulation traffic flow and from the optimization model for a given optimally located MLC advance warning under various traffic regimes. The proposed approach can be implemented by roadside mobile warning facility or on-board GPS for human-driven vehicles, or embedded into lane change aid systems to serve connected and automated vehicles. Thus it will greatly contribute to both literature and engineering practice in lane change management.

Wave energy: Modeling and Analysis of Power Grid Integration

Wave energy could play a major role for diversification of the energy matrix in Latin America. However, it has impact on the stability of the power system. This paper studies the integration of a wave generation system in a power grid and its impact on the oscillations of frequency. A critical analysis is made about the real potential of this technology. Different cases are analyzed taking into account the injection level of power from the wave generator and the requirement of energy storage. Results demonstrate that high penetration of wave generation affects the frequency of the network and takes it out from the dead band considered in the Colombian regulation. Simulations on the IEEE 9 bus system shows that integration of a wave power generation system produces frequency drop, phase power and voltage oscillation as well as other dynamic problems in the power grid. However, when such integration is adequately planned, it is safe to inject power to the electrical system from a wave generation plant.

Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow**Project supported by the National Natural Science Foundation of China (Grant No. 11572062), the Fundamental Research Funds for the Central Universities, China (Grant No. CDJZR13248801), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13043), and Key Laboratory of Functional Crystals and Laser Technology, TIPC, Chinese Academy

We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model.

Surface tension and viscosity of nuclei in liquid drop model

An analytical solution for the capillary oscillations of the charged drop in dielectric medium obtained with taking into account the damping due to viscosity. The model has been applied for the estimation of even-even spherical nuclei surface tension and nuclei viscosity. Attenuation factor to nuclear capillary oscillation frequency ratio has been found.

Numerical investigation of phase relationships in an oscillating sessile drop

Forced linear oscillations of a viscous drop placed on a horizontal surface vibrating in perpendicular direction are investigated. The problem is solved for two cases: (1) constant contact angle, and (2) pinned contact line. Phase-frequency and amplitude-frequency characteristics of oscillations of the drop apex are found for the first axisymmetrical mode of oscillations. The independence of the difference of oscillation phases of the drop apex and the substrate on fluid density, viscosity, surface tension, and drop size as well as on presence or absence of the gravity force was demonstrated.

Experimental investigation on flow instability of forced circulation in a mini-rectangular channel under rolling motion

An experimental study was performed in a mini-rectangular channel under rolling condition to investigate the flow instability of forced circulation. In order to analyze the influence of rolling motion on two-phase flow instability, experiments under both static condition and rolling condition were conducted using the same thermodynamic parameters, such as flow rate, system pressure and inlet fluid temperature. During the experiments, typical pressure drop oscillation (PDO) was observed in static condition, while abundant experimental phenomena including single-phase flow fluctuation, trough-type flow oscillation, coupled flow oscillation and two-phase flow fluctuation were found in rolling condition. Single-phase flow fluctuation, which fluctuates in sinusoidal wave, is directly induced by rolling motion, while two-phase flow fluctuation is supposed to be in annular flow regime which is accompanied with fluctuation caused by rolling motion. Trough-type flow oscillation is confirmed as the boiling incipience according to the pressure drop and heat transfer characteristics. As intermittent boiling occurs at the section close to the outlet of the test channel, during trough-type flow oscillation, two wave peaks in one rolling period are found in the pressure drop fluctuation of the outlet section of the channel. The method of Fast Fourier Transform (FFT) is used to analyze the coupled flow oscillation, and two frequencies, including the rolling frequency and PDO frequency, are found in the amplitude spectrum. Thus, the coupled flow oscillation is supposed to be superposition of trough-type flow oscillation and PDO. Besides, the coupling mechanisms of the coupled flow oscillation are discussed and the evolution characteristics of flow instabilities are presented.

Shape and oscillations of the water drops freely suspended in a horizontal electric field: A wind tunnel study

The time-averaged axis ratios, frequency and amplitude of oscillations of water drops of 2.67–6.6mm diameter were determined by suspending them in a vertical wind tunnel in the absence and presence of horizontal electric fields using a high speed camera at 1000 frames per second. A systematic decrease in the drop's axis-ratio is observed with increase in its diameter and/or horizontal electric field. The results revealed with high speed photography are in good agreement with earlier results. The drop distortion due to horizontal electric field is more pronounced for the drops in the size-range of 3.36–6mm diameter showing that the electrical forces progressively enhance the horizontal elongation of the drop resulting in its instability at 6.6mm. The drop oscillation frequency computed from temporal variation of axis ratio, decreases with increase in drop size but shows no significant change in oscillation frequency in the horizontal electric field of ≤500kVm−1. However, the oscillation amplitude increases with increase in drop size up to a threshold value and then flatten-off in the electric field of ≤300kVm−1 demonstrating the nonlinear effect of net forces acting on such large drops. In higher electric field of 500kVm–1, gradual increase in the amplitude of oscillation with an increase in drop diameter has been observed. Moreover, for a particular drop size, the amplitude of oscillation decreases with increase in the electric field upto 500kVm−1. The oscillation frequency of the waterdrops experiences multimode oscillations. The dominant fundamental mode of oscillations (2,0) always exists for all drops in our experiments along with the coexistence of higher modes of oscillations i.e. (2,1) and (2,2) mode. Possible effects of electrical forces on shape parameters and their implications on cloud microphysics and in radar meteorology are discussed.

Numerical Study for Shape Oscillation of Free Viscoelastic Drop Using the Arbitrary Lagrangian-Eulerian Method

The free oscillation of liquid droplet is one of the classical questions in science research, liquid drops play important role in a lot of engineering applications. Theory study of droplet oscillation mainly based on the linear method, this method is only adapted to the small-amplitude oscillatory motion of drops. Except the linear method used in this study, numerical method have been successfully applied in simulation of the free oscillation of liquid droplet. In this paper, the finite element method is used to investigate numerically the influence of viscoelasticity on the small-amplitude oscillation of drop of polymer solutions. A spatial discretization is accomplished by the finite element method, the time descretization is carried by the Crank-Nicolson method, and the arbitrary Lagangian-Eulerian (ALE) method is used to track the change of the interface. Numerical results are compared with the ones of linear theory. The behaviors of oscillation are found to depend on the viscosity and the stress relaxation time of viscoelastic fluid, the results of numerical simulation and linear theory are identical.